tolerancing

1. Dimensioning and Tolerancing
Design representation:
enough information to
manufacture the part precisely
inspect the manufactured part
[geomtery, dimensions, tolerances]

2. Projections
Theoretical technique to map 3D objects to 2D
Dimensions
To assist machinist:
e.g. distance between centers of holes
Tolerances
imprecision in machining 
must specify the tolerance range,

3. What is a ‘good level of tolerance’?
Designer: tight tolerance is better
(less vibration, less wear, less noise)
Machinist: large tolerances is better
(easier to machine, faster to produce,
easier to assemble)
Tolerances  interchangeability

4. Tolerance and Concurrent Engineering
Why ?
Tolerance specification needs knowledge of
accuracy, repeatability of machines
process capability
…

5. Part 1. Projections.
3D models: expensive, difficult to make
=> need 2D representaitons
Images must convey feasible 3D objects

6. Albrecht Durer’s machine [14??AD] (perspective map)

7. 1. Renaissance architects
2. Modern CAD systems
(a) 3D rendering, image processing
(b) Mathematics of free-form surfaces (NURBS)
Importance of perspective maps

8. Why perspective maps ?
larger, farther  same image size
same size, farther  smaller image
Human sight and perception

9. parallel lines converge to a point
The vanishing point (or station point)

10. Effect of vanishing point on perspective map
Image on the ‘picture plane’ is a perspective of the 3D object
[Is the object behind in perspective view ?]

11. parallel
parallel
parallel
parallel
converge:
finite vanishing point
converge:
finite vanishing point
parallel
parallel
parallel
parallel
parallel
parallel
parallel
converge:
finite vanishing point
converge:
finite vanishing point
parallel
converge:
finite vanishing point
converge:
finite vanishing point
Perspectives and vanishing points
Perspectives in mechanical drafting Not good !
(1) parallel lines converge  misinterpreted by the machinist
(2) Views have too many lines

12. Orthographic views
A mapping where parallel lines remain parallel
How ?
Set the vanishing point at infinity
Another problem:
Back, Sides of object not visible (hidden surfaces)
Solution: Multiple views

13. Orthographic views:
Language of engineering communication

14. View direction selection in orthographics
Maximize true-size view of most faces
FRONT
TOP
RIGHT
FRONT
TOP
RIGHT

15. Isometric view: gives a ‘3D image’
each side has equal length
(a) orthograhic (b) top view rotated by 45° (c) Isometric projection
each side has equal length
(a) orthograhic (b) top view rotated by 45° (c) Isometric projection

16. Different types of projections
All engineering drawings must be made to scale

17. Datum: A theoretical geometric object
(point, line, axis, or plane) derived from
a specific part/feature of a datum feature on the part.
Uses:
(1) specify distance of a feature from the datum
(2) specify a geometric characteristic (e.g. straightness)
of a feature
Part 2. ANSI dimensioning

18. Basic Dimension:
The theoretically exact size of a feature or datum
Feature:
A geometric entity on the part, (hole, axis, plane, edge)
Datum feature:
An actual feature of a part, that is used to establish a datum.

19. Limits: The max/min allowable sizes
Largest allowable size: upper limit
Least allowable size: lower limit.
LMC (Least Material Condition)
MMC (Maximum material Condition)

20. Conventions for dimensioning
(a) Specify tolerance for all dimensions
(b) All necessary , sufficient dimensions
X over-dimensioned X
X under-dimensioned X
Reference dimensions:
Redundant dimensions, in ( …)
(c) Dimensions should be
(i) marked off the datum feature
(ii) shown in true-size view
(iii) shown in visible view

22. (a) Size of a feature
Specified by a basic size, and tolerance: 2.50±0.03
upper limit =
lower limit =
No of digits after decimal  precision
Part 3. Mechanical Tolerancing
Conventional Tolerancing:

23. Unilateral and Bilateral Tolerances:
2.50
+0.03
- 0.03
+0.06
+ 0.00
2.47
-0.00
-0.06
2.53
2.49
+0.04
- 0.02
bilateral unilateral
-0.03
-0.09
2.56
2.50
+0.03
- 0.03
2.50
+0.03
- 0.03
+0.06
+ 0.00
2.47
+0.06
+ 0.00
2.47
-0.00
-0.06
2.53
-0.00
-0.06
2.53
2.49
+0.04
- 0.02
2.49
+0.04
- 0.02
bilateral unilateral
-0.03
-0.09
2.56
-0.03
-0.09
2.56

24. (b) The type of fit between mating features
Designer needs to specify
basic dia, tol of shaft: S±s/2
basic dia, tol of hole: H±h/2
Allowance: a = Dhmin – Dsmax.
Conventional Tolerancing..

25. 0.0006d1/3
0.0006d1/3
-0.001d
Shrink
0.0006d1/3
0.0006d1/3
-0.0005d
Medium Force
0.0006d1/3
0.0006d1/3
-0.00025d
Tight
Interference
[difficult assembly
can transmit torque]
0.0004d1/3
0.0006d1/3
0
Wringing
0.0004d1/3
0.0006d1/3
0
Snug
Transition
[difficult to mfg
precision fit
0.0018d1/3
0.0018d1/3
0.0009d2/3
Medium
0.0013d1/3
0.0013d1/3
0.0014d2/3
Free
0.0025d1/3
0.0025d1/3
0.0025d2/3
Loose
Clearance
[easy assembly,
may vibrate in use]
s (shaft tolerance)
h (hole tolerance)
a (allowance)
Sub-Type
FIT
0.0006d1/3
0.0006d1/3
-0.001d
Shrink
0.0006d1/3
0.0006d1/3
-0.0005d
Medium Force
0.0006d1/3
0.0006d1/3
-0.00025d
Tight
Interference
[difficult assembly
can transmit torque]
0.0004d1/3
0.0006d1/3
0
Wringing
0.0004d1/3
0.0006d1/3
0
Snug
Transition
[difficult to mfg
precision fit
0.0018d1/3
0.0018d1/3
0.0009d2/3
Medium
0.0013d1/3
0.0013d1/3
0.0014d2/3
Free
0.0025d1/3
0.0025d1/3
0.0025d2/3
Loose
Clearance
[easy assembly,
may vibrate in use]
s (shaft tolerance)
h (hole tolerance)
a (allowance)
Sub-Type
FIT
Standard fits

26. The hole-basic specification convention
shaft hole
2.000
+
-
h
a
s
basic
size
hole basic
unilateral tolerance
clearance fit
+
-
h
a
s
basic
size
hole basic
bilateral tolerance
clearance fit
mean
size
+
-
h
a
s
basic
size
hole basic
unilateral tolerance
interference fit
+
-
h
a
s
basic
size
shaft basic
bilateral tolerance
interference fit
mean
size
+
-
shaft hole
2.000
+
-
h
a
s
basic
size
hole basic
unilateral tolerance
clearance fit
+
-
h
a
s
basic
size
hole basic
bilateral tolerance
clearance fit
mean
size
+
-
h
a
s
basic
size
hole basic
unilateral tolerance
interference fit
+
-
h
a
s
basic
size
shaft basic
bilateral tolerance
interference fit
mean
size
+
-
[Holes are made by drills]

27. Generalization of hole-basic/shaft-basic
MMC: Maximum material condition
LMC: Least material condition
Hole at MMC  at the lower limit
Hole at LMC  at the upper limit

28. Geometric Tolerancing
Y
X
t
t
max tol = t 2
Y
X
t
t
max tol = t 2
Problems in Conventional tolerancing:
(a) Assumes perfect surfaces
(b) No use of Datums
(c) No specification of form tolerances
(d) X±t/2, Y±t/2  rectangular tolerance zone (cylindrical preferred)

29. Datums
A theoretical feature (e.g. plane, line)
Serves as a global coordinate frame for the part
during different activities such as
design, manufacturing and inspection.
Each design must specify the datum planes
(or other datums)

30. Datum feature
The actual plane on the part (imperfect)
corresponding to a (perfect) datum plane
datum feature A
datum plane A
datum feature B
datum plane B
datum A
datum B datum C
datum feature A
datum plane A
datum feature B
datum plane B
datum feature B
datum plane B
datum A
datum B datum C
datum A
datum B datum C
Sequence of establishing datums:
PRIMARY (3 points)  SECONDARY (2 points)  TERTIARY (1 point)

31. ANSI symbols for geometric tolerancing
True Position
Location
Total runout
Circular runout
Runout
Concentricity
Parallel
Perpendicular
Angle
Orientation
Surface profile
Line profile
Profile
Cylindricity
Circularity
Flatness
Straightness
Form
Symbol
Characteristic
Type of Tolerance
True Position
Location
Total runout
Circular runout
Runout
Concentricity
Parallel
Perpendicular
Angle
Orientation
Surface profile
Line profile
Profile
Cylindricity
Circularity
Flatness
Straightness
Form
Symbol
Characteristic
Type of Tolerance
MMC
Arc length
Reference size
Spherical Radius
Radius
Spherical Diameter
Diameter
Projected Tol Zone
LMC
Regardless of feature size
ANSI modification symbols
MMC
Arc length
Reference size
Spherical Radius
Radius
Spherical Diameter
Diameter
Projected Tol Zone
LMC
Regardless of feature size
ANSI modification symbols
M
M
S
S
L
L
P
P
S
S
R
SR
( )

32. 3.00
-A-
symbol tolerance modifier datum modifier
0.001 M M
A
datum
basic size
symbol tolerance primary- secondary- tertiary datum
0.001 A B C
3.00
-A-
symbol tolerance modifier datum modifier
0.001 M M
A
symbol tolerance modifier datum modifier
0.001 M M
A
0.001 M
M M
M
A
datum
basic size
symbol tolerance primary- secondary- tertiary datum
0.001 A B C
symbol tolerance primary- secondary- tertiary datum
0.001 A B C
Different allowed notations (ANSI)

33. Location tolerances:
Conventional system:
rectangular tolerance zones
True Position Tolerancing
circular (cylindrical) tolerance zone

34. Form Tolerances

35. Form Tolerances

36. Form Tolerances